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| We study a class of reaction-diffusion models that can be taken as basic models for the dynamics of criminal activity. In this talk I will first discuss the existence of steady-state solutions and discuss the condition that determine whether there there are one, two, or three steady-states. The latter case corresponds to a bi-stable system and in this case we prove the existence of traveling wave solutions in one dimension. Physically, this correspond to the invasion of 'hotspots' into areas that have naturally low crime rates. I will also discuss some numerical results on obstruction of wave propagation. |
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